Enter a radius and angle in degrees to calculate the circular sector.
Choose which two measurements you know. The solver derives radius, central angle, arc length, area, chord and sagitta The main sector workflow above remains available; this panel handles inverse cases.
Angles are reported in degrees; trigonometric formulas are evaluated in radians.
Calculate sector area, arc length, chord, segment area, sagitta and perimeter with degree/radian evidence and an SVG cross-check.
Keep linear inputs in a consistent unit, verify that side lengths or coordinate points can form the stated shape, and treat sketches as explanatory unless explicitly marked to scale. Coordinate formulas can become unstable for nearly degenerate shapes, so invalid or nearly collinear inputs are rejected rather than silently returning misleading values.
Use the interactive product above first. These notes add interpretation, verification and limits below the results and product controls.
Radius and central angle are the most direct pair, but radius with arc length, radius with area, angle with arc length, angle with area, or arc length with area can also determine a sector when the values are positive and geometrically consistent.
Arc length uses L = rθ and sector area uses A = ½r²θ when θ is in radians. A common error is to insert a degree value directly into those equations without first converting it to radians.
The chord joins the two arc endpoints, while the sagitta is the maximum distance from that chord to the arc. They are useful checks, but neither should be substituted for arc length in a curved-edge measurement.
A sector above 180 degrees is the major sector rather than the smaller slice most diagrams suggest. Confirm whether the job, drawing or assignment expects the minor or major region before interpreting area and segment results.
Intermediate rounding can noticeably move chord, sagitta or area results. Keep full precision through angle conversion and trigonometric steps, then round the final dimensions to the accuracy justified by the input measurements.
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